Intrinsic Zeeman Effect in Graphene

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Author(s)

Abstract

The intrinsic Zeeman energy is precisely one half of the cyclotron energy for electrons in graphene. As a result a Landau-level mixing occurs to create the energy spectrum comprised of the 4j-fold degenerated zero-energy level and 4-fold degenerated nonzero-energy levels in the j-layer graphene, where j=1, 2, 3 for monolayer, bilayer and trilayer, respectively. The degeneracy manifests itself in the quantum Hall (QH) effect. We study how the degeneracy is removed by the Coulomb interactions. With respect to the zero-energy level, an excitonic gap opens by making a BCS-type condensation of electron-hole pairs at the filling factor ν=0. It gives birth to the Ising QH ferromagnet at ν=±1 for monolayer, ν=±1, ±3 for bilayer, and ν=±1, ±3, ±5 for trilayer graphene from the zero-energy degeneracy. With respect to the nonzero-energy level, a remarkable consequence is derived that the effective Coulomb potential depends on spins, since a single energy level contains up-spin and down-spin electrons belonging to different Landau levels. The spin-dependent Coulomb interaction leads to the valley polarization at ν=±4, ±8, ±12, ...for monolayer, ν=±2, ±6, ±10, ...for bilayer, and ν=±2, ±4, ±8, ±12, ...for trilayer graphene.

Journal

  • Journal of the Physical Society of Japan

    Journal of the Physical Society of Japan 76(9), "94701-1"-"94701-12", 2007-09-15

    The Physical Society of Japan (JPS)

References:  38

Codes

  • NII Article ID (NAID)
    110006418604
  • NII NACSIS-CAT ID (NCID)
    AA00704814
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00319015
  • NDL Article ID
    8907340
  • NDL Source Classification
    ZM35(科学技術--物理学)
  • NDL Call No.
    Z53-A404
  • Data Source
    CJP  NDL  NII-ELS 
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